Weird Maths in Focus Question (1 Viewer)

[Smilebuffalo]

This question is really weird to me, i can't get the answer.

The question is: "twelve differently coloured beads are arranged around a necklace. How many different arrangements are possible?"

Answer:19,958,400

 

[Aerath]

Answer is 11! / 2. [I only noticed this cause my answer was double the given answer]

But I would've thought it'd just be 11!. Someone explain please?

 

[Revacious]

maybe because... when you flip the necklace over, you get the other half of the solutions

so you only need 11!/2, because the other arrangements occur when you flip it over? haha.

 

[x3.eddayyeeee]

maybe because... when you flip the necklace over, you get the other half of the solutions

so you only need 11!/2, because the other arrangements occur when you flip it over? haha.

thats why.

 

[gurmies]

Yep, that's the correct reasoning. When I first saw this question myself I found it really quaint...

 

[addikaye03]

yep, when dealing with necklaces its (n-1)!/2

 

[Revacious]

haha necklaces are in their own separate category; why isnt there an arrangements on a necklace chapter in any of these stupid books.

i think its a stupid question.

 

[gurmies]

Likewise, lol. One could argue you could flip over a table with people sitting on it...wouldn't be overly comfortable xD

 

[Smilebuffalo]

LOL okay. But i don't understand why "when you flip the necklace over, you get the other half of the solutions". What does this mean and how is it different from a circle? :\

Sorry i find these concepts a bit hard to grasp.

 

[studybuddy09]

I think you should go buy some twine and thread some different coloured beads on and see what happens when you flip it.

If you cant be bothered i can just tell you that when you flip a necklace it reverses, so it would form a different pattern, thereby excluding the need for making that pattern again.

i might be wrong though but i dont think so. hope this helps

 

[Revacious]

LOL okay. But i don't understand why "when you flip the necklace over, you get the other half of the solutions". What does this mean and how is it different from a circle? :\

Sorry i find these concepts a bit hard to grasp.

well just think of it like
you have 4 beads on a necklace

so there should be 6 ways to arrange them

but for instance, one particular arrangement

A B C D (in a clockwise direction) is equivalent to A C B D once the thing is flipped over.

you can only flip it twice, flipping it more obviously yields nothing, so you need to divide by two.

 

[Smilebuffalo]

oooooh cool. I get it now. Thanks a lot! !

 

[mitchy_boy]

gotta love maths in focus and their useful question.